Alternative medicine promotor Deepak Chopra is the latest medical professional to suggest we do. In a series of tweets late Monday – the day FBI director James Comey shot down the president’s unfounded but continuing claims about wiretapping at Trump Tower – Chopra asked Trump to “please submit to a psychiatric and neurological evaluation to restore our confidence.”

Chopra, who trained as an endocrinologist (a hormone specialist), not a psychiatrist or neurologist, also suggested that a form of dementia, a brain disease that affects behavior and thinking, should “be ruled in or ruled out,” “for the safety of the world.”

For the record, Trump’s longtime personal physician Harold Bornstein recently told the health news site Stat that while Trump carries some extra pounds, “there’s nothing seriously wrong with him.” In two letters issued during the campaign, Bornstein also said Trump, 70, was in fine physical health. Bornstein also told The New York Times he probably would not screen Trump for dementia if he became White House physician (so far, he has not).

That has not stopped speculation, especially about Trump’s mental health. Such speculation, at least by psychiatrists, has been officially discouraged by the American Psychiatric Association (APA). Earlier this month, the group updated its longstanding ethics policy against opining on the mental health of politicians or other public figures. The policy is called the Goldwater Rule, after 1964 presidential candidate Barry Goldwater, and was created after many psychiatrists participated in a magazine survey about Goldwater’s mental fitness.

The rule is based partly on the belief that psychiatrists should not diagnose unconsenting people they have not examined. But it also reflects concerns that equating mental health with fitness for certain jobs stigmatizes people with mental illness, said Rebecca Weintraub Brendel, an assistant professor of psychiatry at Harvard Medical School and consultant to the APA’s ethics committee.

“The public doesn’t really need psychiatrists to reach conclusions,” about whether politicians should stay in office, she added.

Despite the policy, 35 psychiatrists, psychologists and social workers signed a letter to the Times in February saying Trump’s “speech and actions demonstrate an inability to tolerate views different from his own, leading to rage reactions.” They said this “grave emotional instability” made him “incapable of serving safely as president.” The letter did not suggest any diagnosis for Trump.

In a separate letter to the Times, Allen Frances, a psychiatry professor emeritus at Duke University School of Medicine, took a different view. He wrote that Trump “may be a world-class narcissist, but this doesn’t make him mentally ill.” Francis said that associating Trump's behavior with mental illness “is a stigmatizing insult to the mentally ill.”

Dear @realDonaldTrump@POTUS Would you please submit to a psychiatric and neurological evaluation to restore our confidence . Thank you Sir

As to whether Trump should undergo the kind of testing Chopra suggests, some experts think all modern presidents should. Arthur Caplan, a bioethicist at New York University's Langone Medical Center, told NPR: "I think we're about 50 years overdue for having some sort of annual physical for the president and vice president, the results of which should be reported publicly. Part of this should be psychiatric and cognitive testing."

But that’s different from suggesting that public concerns generated by a president’s TV appearances and social media posts should trigger psychiatric testing, Weintraub Brendel said. That, she said, would be “a political misuse of psychiatry.”